Inverse kinematics solution using neural networks from forward kinematics equations

Introduction Atmospheric corrosion is the main cause of metallic heritage degradation when they are exposed to relative humidity, temperature cycle and air contaminants. Corrosivity maps are one of the preventive strategies for atmospheric corrosion mitigation, but they do not provide enough information about corrosion mechanism, besides that long experimentation periods are required [1]. Moreover, electrochemical techniques are alternatives to speed up results, but their relationship with constantly changing environmental variables is difficult to control.Currently, Artificial Intelligence has been introduced in corrosion engineering studies, because of its capability to make predictions based on big data. Also, experimental data of Electrochemical Impedance Spectroscopy had been used in Artificial Neural Network training to obtain Nyquist Diagrams [2]. The objective of this work is to obtain computational models of Artificial Neural Networks to predict atmospheric corrosion in Bronze with nanostructured patina with SiO2, in marine environments. Method Environmental parameters were taken from database previously reported [3,4], and from Civil Protection Secretariat of Veracruz. Whilst electrochemical evaluation consists in Polarization Resistance and Electrochemical Impedance Spectroscopy; they were carried out in a Gamry Interface 1000 Potentiostat with a Saturated Calomel Reference Electrode (SCE) and a graphite bar as counter electrode in an agar gelled cell. Meanwhile, working electrode was bronze with nanostructured patina with SiO2. Two patina were prepared, the first with CuSO4 solution (0.015 mol L-1) and the second applying a CuNO3 solution (20% wt).The 13 variables used in the database for Artificial Neural Networks (ANN) training were: exposure time, chloride concentration, sulfur compounds concentration, relative humidity, precipitation level, windspeed, temperature, nanocoating presence, corrosion potential, corrosion rate, frequency, real and imaginary component of impedance. The values of each variable were treated with measures of central tendency and dispersion, as well as correlation matrix and histograms, which allowed to find a relationship between variables, and choosing the inputs for ANN. The prediction models consisted in 5, 9, 10 and 12 neurons in the input layer (R5E, R9E, R10E and R12E, respectively), a hidden layer, and Zima as only neuron in the output layer. The number of neurons in hidden layer varied from 1 to 8 until the highest coefficient of determination was achieved. The computational model was performed using the toolbox in MATLAB with a feedforward ANN. It is worth mention that the hidden and output layers used a hyperbolic tangent and a linear transfer function, respectively, and a Levenberg-Marquardt algorithm as training function was used in the models. Results and Conclusions Figure 1 presents the coefficient of determination (R2) and root mean squared error (RMSE) with different ANN architectures. In the four models, the highest value was reached with 8 neurons in the hidden layer. Then, the linear regressions for R5E, R9E, R10E and R12E models and 8 neurons in the input layer were compared in Figure 2. In that sense, the Nyquist Diagrams in Figure 3 were simulated with the R9E and R12E models. Also, they were compared with experimental Nyquist Diagrams for Bronze with patina of CuSO4 and CuNO3, with and without SiO2 nanoparticles, at 56 days of exposure in marine atmospheres. The simulations demonstrated how an ANN model with 12 neurons in the input layer, 8 neurons in the hidden layer and 1 neuron in the output layer can be used as a corrosion prediction model of bronze with nanostructured patina with SiO2.

This paper examines the architecture of back-propagation neural networks used as approximators by addressing the interrelationship between the number of training pairs and the number of input, output, and hidden layer nodes required for a good approximation. It concentrates on nets with an input layer, one hidden layer, and one output layer. It shows that many of the currently proposed schemes for selecting network architecture for such nets are deficient. It demonstrates in numerous examples that overdetermined neural networks tend to give good approximations over a region of interest, while underdetermined networks give approximations which can satisfy the training pairs but may give poor approximations over that region of interest. A scheme is presented that adjusts the number of hidden layer nodes in a neural network so as to give an overdetermined approximation. The advantages and disadvantages of using multiple output nodes are discussed. Guidelines for selecting the number of output nodes are presented.

Abstract. This paper focuses on the 4-PUU parallel mechanism with Schönflies motion, investigating its kinematic analysis and utilizing intelligent algorithms to solve its forward kinematics equations. Using screw theory as the mathematical framework, the number and nature of the degrees of freedom of the 4-PUU parallel mechanism are analyzed, proving that the mechanism can achieve 3T1R motion. The forward and inverse position kinematics equations are established with link lengths as constraints, and the velocity and acceleration equations of the mechanism are derived using the vector method. The forward kinematics equations of the mechanism are transformed into an unconstrained optimization problem, which is solved using an improved beluga whale optimization (BWO). To enhance the uniformity of the initial population distribution, a chaotic-opposition-based learning initialization strategy is introduced. Additionally, an elite strategy and a golden-sine-based position update mechanism are incorporated to improve the optimization capability of BWO. The integration of these strategies results in an enhanced optimization algorithm with superior global search ability. Given the mechanism's dimensional parameters, theoretical and motion simulations are conducted using MATLAB and Adams. The results indicate that the motion simulation curves from Adams closely match the numerical simulation curves from MATLAB, validating the theoretical derivation. Building on this, the improved beluga whale optimization (IBWO) algorithm, along with comparison algorithms (DEb1, ABC, PSO), is applied to solve the forward kinematics equations for interpolation points along the simulated trajectory. Numerical experiments demonstrate that IBWO outperforms the other comparison algorithms in solving the problem efficiently and accurately.

In this study, an inverse kinematic solution approach applicable to six degree-of-freedom industrial robotic manipulators is introduced. The approach is based on a previously introduced kinematic classification of industrial robotic manipulators by Balkan et al. (1999), and depending on the kinematic structure, either an analytical or a semi-analytical inverse kinematic solution is obtained. The semi-analytical method is named as the parametrized joint variable (PJV) method. Compact forward kinematic equations obtained by utilizing the properties of exponential rotation matrices. In the inverse kinematic solutions of the industrial robots surveyed in the previous study, most of the simplified compact equations can be solved analytically and the remaining few of them can be solved semi-analytically through a numerical solution of a single univariate equation. In these solutions, the singularities and the multiple configurations of the manipulators can be determined easily. By the method employed in this study, the kinematic and inverse kinematic analysis of any manipulator or designed-to-be manipulator can be performed and using the solutions obtained, the inverse kinematics can also be computerized by means of short and fast algorithms. As an example for the demonstration of the applicability of the presented method to manipulators with closed-chains, ABB IRB2000 industrial robot is selected which has a four-bar mechanism for the actuation of the third link, and its compact forward kinematic equations are given as well as the inverse kinematic solution.

In this work, a new approach for parallel-hierarchical (PH) networks learning having applied to the real-time image sequences in extended laser paths is proposed. It is possible to synthesize PH network with learning abilities by using the general idea of artificial neural networks structured organization on the scheme: input layer - hidden layer - output layer. The 1st network level should be used as input layer, next levels should be used as a hidden layer and the last level should be used as an output one, as it is traditionally in artificial neural networks, Using the main PH network feature which determine the length of network algorithm it is possible to determine a number of hidden layer elements. And in this way it formalizes the procedure of obtaining the number of hidden layer elements.

We describe a scheme of emotion prediction from the music songs based on seven acoustic features from three different categories; timbre, rhythm, and dynamics. 20 full-length songs from different genre were selected. Two-dimensional emotion model (arousal-valence model) is adopted. The ratings of arousal and valence for these songs were calculated by multiple linear regression method. Neural network with two different parameter sets were trained by extracted features using 80% of the dataset. The trained network is tested on the remaining 20% of data. First neural network with 7 input layers, the default number of hidden layers (average input and output layers) and 4 output layers did not perform well (50% accuracy). The second neural network with the number of hidden layers equal to the number of input layers and 4 output layers performed a good job with 75% accuracy in predicting the emotion class. The result of the study indicates, that training a neural network can identify the statistical consistencies across acoustic features of music to predict the emotion.

Roughly speaking, knowledge networks are explained from a neural network in which degrees of learning are established, considering the differences between the input layer, the intermediate or hidden layer and the output layer. A non-experimental, cross-sectional and exploratory study was carried out with a non-probabilistic selection of 300 students, managers and teachers from a public university in central Mexico. The results show a factorial asymmetry of one input layer unit for three output layer units, suggesting that there is a significant degree of learning around the knowledge network. However, there are areas of opportunity around the hidden layer, since its units reveal information processing that reduces the uncertainty of the input layer and amplifies the knowledge of the output layer.

– Grosso modo, knowledge networks are explained from a neural network in which degrees of learning are established, considering the differences between the input layer, the intermediate or hidden layer and the output layer. A non-experimental, cross-sectional and exploratory study was carried out with a non-probabilistic selection of 300 students, managers and teachers from a public university in central Mexico. The results show a factorial asymmetry of one input layer unit for three output layer units, suggesting that there is a significant degree of learning around the knowledge network. However, there are areas of opportunity around the hidden layer, since its units reveal information processing that reduces the uncertainty of the input layer and amplifies the knowledge of the output layer.

Summary In this work, the artificial neural network (ANN) is implemented for prediction slug frequency FS for low viscosity μL flow (μL ≤ 1.6 mPa·s) in vertical, horizontal, and inclined pipes. To the authors' knowledge, no ANN model in the literature exists for predicting FS. The input parameters for the suggested ANN are superficial liquid velocity VSL, pipe diameter D, superficial gas velocity VSG, and pipe inclination ϕ. Measured data (450 data points) are gathered from five different resources for developing the ANN model. The ranges of FS, VSL, D, VSG, and ϕ covered by the data set, are (0.03 to 3.167 1/s), (0.05 to 2.073 m/s), (0.01905 to 0.0779 m), (0.133 to 11.84 m/s), and (0 to 90°), respectively. The most popular transfer functions of tangent sigmoid and linear are used in the hidden and output layers, respectively, whereas the Levenberg and Marquardt back propagation algorithm is conducted to train ANN. The experimental data set is divided into 70% for training, 15% for validation, and 15% for testing processes. Due to the absence of a systematic way to find the optimal structure of ANN, an exhaustive search method has been suggested and implemented to find the optimal topology, which is (4-16-1); four neurons in input layer, 16 neurons in the hidden layer, and one neuron in output layer. The proposed ANN predicts correctly the effect of each of the previously mentioned parameters on FS, and it yields a satisfactory prediction and clearly outperforms all the existing models, with a mean square error (MSE) and R2 of 0.0097 and 0.977, respectively.

Now knowledge pre-processing, model and reasoning issues, power metrics, quality issues, post-processing of discovered structures, visualization, and on-line change is best challenge. In this paper Neural Network based forecasting of stock prices of selected sectors under Bombay Stock Exchange show that neural networks have the power to predict prices albeit the volatility in the markets(9). The motivation for the development of neural network technology stemmed from the desire to develop an artificial system that could perform intelligent tasks similar to those performed by the human brain. Artificial Neural Networks are being counted as the wave of the future in computing. They are indeed self-learning mechanisms which don't require the traditional skills of a programmer. Back propagation is one of the approaches to implement concept of neural networks. Back propagation is a form of supervised learning for multi-layer nets. Error data at the output layer is back propagated to earlier ones, allowing incoming weights to these layers to be updated. It is most often used as training algorithm in current neural network applications. In this paper, we apply data mining technology to stock market in order to research the trend of price; it aims to predict the future trend of the stock market and the fluctuation of price. This paper points out the shortage that exists in current traditional statistical analysis in the stock, then makes use of BP neural network algorithm to predict the stock market by establishing a three-tier structure of the neural network, namely input layer, hidden layer and output layer. Finally, we get a better predictive model to improve forecast accuracy.

Comparison of RBF and MLP neural networks to solve inverse kinematic problem for 6R serial robot by a fusion approach

In senior high schools, especially in the first class were required to place a department that is in accordance with the value produced. The application predicts student majors based on the value of students using artificial neural network algorithms using rapid miner to be able to produce more precise and faster accuracy results. The results obtained from the analysis carried out obtained an accuracy value of 71.86%.ANN has a network architecture that is a single layer net. Networks that have more than one layer are called multilayer net and competitive layer networks (competitive layer net). The shape of a multilayer net 1 or more has between the input layer and the output layer, which weighs between 2 adjacent layers. ANN architecture using 3 layers is 7 input layers, 6 hidden layers, and 2 output layers. 20 neurons are the number of neuron outputs to artificial neural networks

Modeling of surface roughness in wire electrical discharge machining of Inconel 718 using artificial neural network

The paper proposes a multifunction charger for LiFePO4 battery. The proposed multifunction charger contains charge circuit for LiFePO4 battery and state of charge (SOC) estimation system. With a micro processor integrated, the proposed charger is capable of digital control to improve the system reliability. The fast charger uses pulse current charging circuit which integrates micro processor, voltage detecting interface, current detecting interface and control software. The user can adjust the duty cycle and frequency of charging pulse by controlling the pulse width modulation (PWM) signal. The proposed battery state of charge estimation system is based on the radial basis function (RBF) neural network approach. The architecture of RBF neural network used in this project contains an input layer, an output layer and a hidden layer. Input layer has 3 neurons which are impedance, voltage, current of battery and output layer has one neuron which is SOC. To verify the performances of the proposed multifunction fast charger, a prototype charger has been tested on practical LiFePO4 battery. The field practical operations of the prototype charger were studied in accordance with the conditions for the different charging modes.

Neural Networks have been used in system control, medicine, pattern recognition and business. The backpropagation neural network (BPNN) appear to be most popular and have been widely used in many applications. BPNN is a supervised learning technique for training multilayer feedforward neural networks. The gradient or steepest descent method is used to train a BPNN by adjusting the weights. The purpose of update numerical weights is minimize error of network between target and output. In this paper, focus with BPNN modeling with data battery for training and testing. We used discharge and Urban Dynamometer Driving Schedule (UDDS) as training data and testing data, respectively Architecture of BPNN consist of input layer, hidden layer and output layer. The otherhand, using BPNN has problem to define amount of hidden neurons. In this study, we used current or voltage as input in input layer, one hidden layer with 8 neurons and one output layer. We used Levenberg-Marquardt algorithm to get fast iteration when...